1. Field of the Invention
This invention relates generally to nuclear reactors, and more particularly to determining pin enrichments in fuel assemblies of a nuclear reactor.
2. Related Art
A boiling water reactor (BWR) or pressurized water reactor (PWR) typically operates from one to two years before requiring fuel replacement. This period is referred to as a fuel cycle or energy cycle. Upon completion of a cycle, approximately ¼ to ½ (typically about ⅓) of the least reactive fuel in the reactor is discharged to a spent fuel pool. The number of fuel assemblies (e.g., fuel bundles) discharged typically are replaced by an equal number of fresh fuel assemblies (e.g., fresh bundles).
The fresh bundles may vary in bundle average enrichment (the average % of enriched uranium (U235) and poisons (such as gadolinium) across the bundle, determined by the total weight of U235 and gadolinia in the bundle divided by the weight of the bundle, local peaking characteristics, exposure peaking, R-factor characteristics, and overall exposure dependent reactivity. Exposure peaking and R-factors are, in fact, functions of local peaking and their behavior may be defined, without loss in generality, by considering local peaking only. The exposure dependent local peaking factor of the fresh bundle may be determined from the maximum local peaking value in any pin (e.g., a pin is a particular fuel rod in a fuel bundle or assembly) of the fresh bundle in question. The higher the local peaking factor, the higher the Maximum Average Planar Linear Heat Generation Rate (MAPLHGR), which is a power related limit on nuclear fuel. Similarly, the R-Factor for the fresh bundle may be determined from the maximum R-Factor in any pin of the fresh bundle in question. When coolant in a core can no longer remove heat at a sufficient rate the fuel and clad temperature will start to increase rapidly. This boiling transition condition may be known as film dryout, burnout, departure from nucleate boiling, depending on the actual conditions leading to the temperature excursion. For BWR fuel, the boiling transition phenomenon may be referred to as dryout. An R-factor value may be a value correlating thermal hydraulic variables (such as flow rate, inlet subcooling, system pressure, hydraulic diameter) to a lattice fuel rod power peaking distribution. The local power in the bundle is a function of the individual rods surrounding an affected rod; thus the weighted local power factor is called an R-factor. Exposure peaking is related to the integral of the local peaking of each individual fuel pin and is constrained by the maximum licensed exposure capability of the fuel.
Because local peaking and R-factor values in any fuel bundle are directly proportional to MAPLHGR limits (KW/ft limits) and minimum critical power ratio (MCPR) limits, it is beneficial to minimize the local peaking and R-factor values while meeting other criteria such as bundle average enrichment, hot-to-cold swing (reactivity excursion at beginning of cycle (BOC) from hot, uncontrolled conditions to cold, controlled conditions), and overall exposure dependent reactivity. Exposure peaking must also be considered at the design time, as a high exposure peaking factor limits the maximum bundle exposure and therefore the maximum reload enrichment that can be loaded in the reactor.
Currently, design engineers utilize “rules of thumb” regarding the relative relationship between enrichment and the dependent effects of local peaking exposure peaking and R-Factor on fuel bundle performance. Therefore, pin enrichments throughout a reactor core are iterated by hand. Resulting bundles would be considered finished even though additional improvements could have been performed. Alternatively, bundle designs would take a large amount of iterations and time to perform.
The current process to make modifications to an existing bundle design to meet the requirements of a core design and operating strategy involves extracting information from a detailed fuel cycle simulation, converting this information into fuel characteristic changes, and then modifying a two-dimensional (2D) enrichment and gadolinium pin placement (e.g., 2D enrichment distribution) to yield these changes. This process is significantly complex, as looping through design iterations is time consuming, since the current code used to implement the rules of thumb and to perform these iterations is inefficient and laborious. A single iteration typically takes from about 4 hours to the better part of a day, with extensive cost in terms of manpower. Thus, very few iterations are typically performed, due to the difficulty and time needed to perform a single iteration using the aforementioned thumb rules and code.
Additionally, designers have become increasingly frustrated as to how inaccurate “rules of thumb” about how changing enrichment in a given pin would effect the resulting local peaking and R-factors for a given bundle (e.g., secondary effects). Because a large number of fresh fuel bundles are typically required for a given fuel cycle, if the “rule of thumb” used in the iterations is erroneous, which frequently may be the case, the efforts and man hours used to model the bundle are wasted. Accordingly, the resulting core design of fresh fuel assemblies for a prospective fuel cycle may not be as effective as it could be in minimizing the local peaking and R-factor while meeting other criteria such as bundle average enrichment, hot-to-cold swing, and overall exposure dependent reactivity.